Multi-parameter Continuous Mean Family In Higher Space

The research for the means has a long history, the classical means include algebraic mean, geometric mean and harmonic mean etc. During the development of theory of mean, the theory of mean family is built. In this theory, a lot of related concepts are introduced and a significant theorem is proved.This paper is based on continuous mean family with single parameter which is in real number space, and builds multi-parameter continuous mean family in higher space. According to the difference of the space, two types of mean functional sets and two types of mean operator set are defined.This paper can be divided into four parts by the types of sets. Properties are researched detailedly in each part. The definitions of one-parameter continuous mean families of several variables , multi-parameter continuous mean families of several variables and ordered mean families are given in the sets. With the change of position which the parameters act on, we can get many mean functional families.